Mastering Physics Solutions Chapter 30 Quantum Physics
Chapter 30 Quantum Physics Q.1CQ
Give a brief description of the “ultraviolet catastrophe.”
Solution:
Chapter 30 Quantum Physics Q.1P
CE Predict/Explain The blackbody spectrum of blackbody A peaks at a longer wavelength than that of blackbody B. (a) Is the temperature of blackbody A higher than or lower than the temperature of blackbody B? (b) Choose the best explanation from among the following:
- Blackbody A has the higher temperature because the higher the temperaturethe longer the wavelength.
- Blackbody B has the highertemperature because an increase in temperature means an increase in frequency, which corresponds to a decrease in wavelength.
Solution:
Chapter 30 Quantum Physics Q.2CQ
How does Planck’s hypothesis of energy quantization resolve the “ultraviolet catastrophe”?
Solution:
Chapter 30 Quantum Physics Q.2P
The Surface Temperature of Betelgense Betelgeuse, a red-giant star in the constellation Orion, has a peak in its radiation at a frequency of 1.82 × 1014 Hz. What is the surface temperature of Betelgeuse?
Solution:
Chapter 30 Quantum Physics Q.3CQ
Is there a lowest temperaturebelow which blackbody radiation is no longer given off by an object? Explain.
Solution:
Chapter 30 Quantum Physics Q.3P
What is the frequency of the most intense radiation emitted by your body? Assume a skin temperature of 95 °F. What is the wavelength of this radiation?
Solution:
Chapter 30 Quantum Physics Q.4CQ
How can an understanding of blackbody radiationallow us to determinethe temperature ofdistant stars?
Solution:
Chapter 30 Quantum Physics Q.4P
The Cosmic Background Radiation Outer space is filled with a sea of photons, created in the early moments of the universe. The frequency distribution of this “cosmic background radiation” matches that of a blackbody at a temperature near 2.7 K. (a) What is the peak frequency of this radiation? (b) What is the wavelength that corresponds to the peak frequency?
Solution:
Chapter 30 Quantum Physics Q.5CQ
Different Fading Many vehicles inthe United States have a small American flag decal inone of their windows. If the decal has been in place for a long time, the colors will show some
Differential fading, (Conceptual Question 5)
fading from exposure to the Sun. In fact, the red stripes are generally more faded than the blue background for the stars, as shown in the accompanying photo. Photographs and posters react in the same way, with red colors showing the most fading. Explain this effect in terms of the photon model of light.
Solution:
Chapter 30 Quantum Physics Q.5P
The Sun has a surface temperature of about 5800 K. At what frequency does the Sun emit the most radiation?
Solution:
Chapter 30 Quantum Physics Q.6CQ
Asource of light is monochromatic. What can you say about the photons emitted by this source?
Solution:
Chapter 30 Quantum Physics Q.6P
(a) By what factor does the peak frequency change if the Kelvin tempera ture of an object is doubled from 20.0 K to 40.0 K? (b) By what factor does the peak frequency change if the Celsius temperature of an object is doubled from 20.0 °C to 40.0 °C?
Solution:
Chapter 30 Quantum Physics Q.7CQ
The relative Intensity of radiation, given off by a blackbody is shown in Figure 30–2. Notice that curves corresponding to different temperatures never cross one another. If two such curves did intersect, however, it would be possible to violate the second law of thermodynamics. Explain.
Solution:
Chapter 30 Quantum Physics Q.7P
IP A Famous Double Star Albireo in the constellation Cygnus, which appears as a single star to the naked eye, is actually a beautiful double-star system. The brighter of the two stars is referred to as A (or Beta-01 Cygni), with a surface tempera ture of TA = 4700 K; its companion is B (or Beta-02 Cygni), with a surface temperature of TB = 13,000 K. (a) When viewed througha telescope, one star is a brilliant blue color, and the other has a warm golden color, as shown in the accompanying photo. Is the blue star A or B? Explain, (b) What is the ratio of the peak frequencies emitted by the two stars, (fA/fB)?
Solution:
=0.3615
Chapter 30 Quantum Physics Q.8CQ
(a) Is it possible for a photon from a green source of light to have more energy than a photon from a blue source of light? Explain, (b) Is it possible for a photon from a green source oflight to have more energy than a photon from a red source of light? Explain.
Solution:
Chapter 30 Quantum Physics Q.8P
IP Halogen Lightbulbs Modern halogen lightbulbs allow their filaments to operate at a highertemperature than the filaments in standard Incandescent bulbs. For comparison, the filament in a standard lightbulb operates at about 2900 K, whereas the filament ina halogen bulb may operate at 3400 K.
(a) Which bulb has the higher peak frequency? (b) Calculate the ratio of peak frequencies (f hal/f std). (c) The humaneye is most sensitive to a frequency around 5.5 × 1014 Hz. Which bulb produces a peak frequency closer to this value?
Solution:
Chapter 30 Quantum Physics Q.9CQ
Light of a given wavelength ejects electrons from the surfaceof one metal but not from the surface of another metal. Give a possible explanation for this observation.
Solution:
Chapter 30 Quantum Physics Q.9P
IP A typical lightbulb contains a tungsten filament that reaches a temperature of about 2850 K, roughly half the surface temperatureof the Sun. (a) Treating the filament as a blackbody, determine the frequency for which its radiation is a maximum. (b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.
Solution:
Chapter 30 Quantum Physics Q.10CQ
Why does the existence of a cutoff frequency inthe photoelectric effect argue in favor of the photon model of light?
Solution:
Chapter 30 Quantum Physics Q.10P
Exciting au Oxygen Molecule An oxygen molecule (O2) vibrates with an energy identical to that of a single particle of mass m = 1.340 × 10−26 kg attached to a spring with a force constant of k = 1215 N/m. The energy levels of the system are uniformly spaced, as indicated in Figure 20, with a separation given by hf. (a) What is the vibration frequency of this molecule? (b) How much energy must be added to the molecule to excite it from one energy level to the next higher level?
Solution:
Chapter 30 Quantum Physics Q.11CQ
Why can an electron microscope resolve, smaller objects than a light microscope?
Solution:
Chapter 30 Quantum Physics Q.11P
CE source of red light, a source of green light, and a source of blue light each produce beams of light with the same power. Rank these sources in order of increasing (a) wavelength of light, (b) frequency of light, and (c) number of photons emitted per second. Indicate ties where appropriate.
Solution:
Chapter 30 Quantum Physics Q.12CQ
A proton is about 2000 times more massive than an electron. Is it possible for an electron to have the same de Broglie wavelength as a proton? Explain.
Solution:
Chapter 30 Quantum Physics Q.12P
CE Predict/Explain A source of red light has a higher-wattage than a source of green light. (a) Is the energy of photons emitted by the red source greater than, less than, or equal to the energy of photons emitted by the green source? (b) Choose the best explanation from among the following:
I. The photons emitted by the red source have the greater energy because that source has the greater wattage.
II. The red-source photons have less energy than the green-source photons because they have a lower frequency. The wattage of the source doesn’t matter.
III. Photons from the red source have a lower frequency, but that source also has a greater wattage. The two effects cancel, so the photons have equal energy.
Solution:
Chapter 30 Quantum Physics Q.13P
CE Predict/Explain A source of yellow light has a higher-wattage than a source of blue light. (a) Is the number of photons emitted per second by the yellow source greater than, less than, or equal to the number of photons emitted per second by the blue source? (b) Choose the test explanation from among the following:
- The yellow source emits more photons per second because
- it emits more energy per second than the blue source, and
- its photons have less energy than those of the blue source.
- The yellow source has the higher wattage, which means its photons have higher energy than the blue-source photons. Therefore, the yellow source emits fewer photons per second.
- The two sources emit the same number of photons per second because the higher wattage of the yellow source compensates for the higher energy of the blue photons.
Solution:
Chapter 30 Quantum Physics Q.14P
CE Predict/Explain Light of a particular wavelength does not eject electrons from the surface of a given metal, (a) Should the wavelength of the light be increased or decreased in order to cause electrons to be ejected? (b) Choose the best explanation from among the following:
- The photons have too little energy to eject electrons. To increase their energy, their wavelength should be Increased.
- The energy of a photon is proportional to its frequency; that is, inversely proportional to its wavelength. To increase the energy of the photons so they can eject electrons, one must decrease their wavelength.
Solution:
Chapter 30 Quantum Physics Q.15P
CE Light of a particular wavelength and intensity does not eject efectrons from the surface of a given metal. Can electrons be ejected from the metal by increasing the intensity of the light? Explain.
Solution:
Chapter 30 Quantum Physics Q.16P
When a person visits the local tanning salon, they absorb photons of ultraviolet (UV) light to get the desired tan. What are the frequency and wavelength of a LJV photon whose energy is 6.5 × 10−19 J?
Solution:
Chapter 30 Quantum Physics Q.17P
An AM radio station operating at a frequency of 880 kHz radiates 270 kW of power from its antenna. How many photons are emitted by the antenna every second?
Solution:
Chapter 30 Quantum Physics Q.18P
Aphoton with a wavelength of less than 50.4 ran can ionize a helium atom. What is the ionization potential of helium?
Solution:
Chapter 30 Quantum Physics Q.19P
Aflashlight emits 2.5 W of light energy. Assuming a frequency of 5.2 × 1014 Hz for the light, determine the number of photons given off by the flashlight per second.
Solution:
Chapter 30 Quantum Physics Q.20P
Light of frequency 9.95 × 1014 Hz ejects electrons from the surface of silver. If the maximum kinetic energy of the ejected electrons is 0.180 × 10−19 J, what is the work function of silver?
Solution:
Chapter 30 Quantum Physics Q.21P
The work function of gold is 4.58 eV. What frequency of light must be used to eject electrons from a gold surface with a maximum kinetic energy of 6.48 × 10−19 J?
Solution:
Chapter 30 Quantum Physics Q.22P
(a) How many 350-nm (UV) photons- are needed to provide a total energy of 2.5 J? (b) How many 750-nm (red) photons are needed to provide the same energy?
Solution:
Chapter 30 Quantum Physics Q.23P
(a) Mow many photons per second are emitted by a monochromatic lightbulb (λ = 650 nm) that emits 45 W of power? (b) If you stand 15 m from this bulb, how many photons enter each of your eyes per second? Assume your pupil is 5.0 mm in diameter and that the bulb radiates uniformly in all directions.
Solution:
Chapter 30 Quantum Physics Q.24P
IP Two 57.5-kW radio stations broadcast at different frequencies. Station A broadcasts ata frequency of 892 kHz, and station B broadcasts at a frequency of 1410 kHz. (a) Which station emits more photons per second? Explain, (b) Which station emits photons of higher energy?
Solution:
Chapter 30 Quantum Physics Q.25P
Dissociating the Hydrogen Molecule The energy required to separate a hydrogen molecule into its individual atoms is 104.2 kcal per mole of H2. (a) If the dissociation energy for a single H2 molecule is provided by one photon, determine its frequency and wavelength. (b) In what region of the electromagnetic spectrum does the photon found in part (a) lie? (Refer to the spectrum shown in Figure 25–8.)
Solution:
Chapter 30 Quantum Physics Q.26P
(a) How many photons are emitted per second by a He-Ne laser that emits 1.0 mW of power at a wavelength λ = 632.8 nm? (b) What is the frequency of the electromagnetic waves emitted by a He-Ne laser?
Solution:
Chapter 30 Quantum Physics Q.27P
IP You have two lightbulbs of different power and color, as indicated in Figure30-21. One is a 150-W red bulb, and the other is a 25-W blue bulb. (a) Which bulb emits more photons per second? (b) Which bulb emits photons of higher energy? (c) Calculate the number of photons emitted per second by each bulb. Take λred = 650 nm and λb1ue = 460 nm. (Most of the electromagnetic radiation given off by incandescent lightbulbs is in
FIGURE 10–11 Problem 27
the infrared portion of the spectrum. For the purposes of trug problem, however, assume that all of the radiated power is at the wavelengths indicated.)
Solution:
Chapter 30 Quantum Physics Q.28P
The maximum wavelength an electromagnetic wave can have and still eject an electron from a copper surface is 264 nm. What is the work functionof a copper surface?
Solution:
Chapter 30 Quantum Physics Q.29P
IP Aluminum and calcium have photoelectric work functions of WAI = 4.28 eV and WCa, = 2.87 eV, respectively, (a) Which metal requireshigher-frequency light to produce photoelectrons? Explain, (b) Calculate the minimum frequency that will produce photoelectrons from each surface.
Solution:
Chapter 30 Quantum Physics Q.30P
IP Two beams of light with different wavelengths (λA > λB) are used to produce photoelectrons from a given metal surface, (a) Which beam produces photoelectrons with greater kinetic energy? Explain, (b) Find Kmax for cesium (W0 = 1.9 eV) if λA = 620 nm and λB = 410 nm.
Solution:
Chapter 30 Quantum Physics Q.31P
IP Zinc and cadmium have photoelectric work functions given by WZn = 4.33 eV and WCd = 4.22 cV, respectively, (a) If both metals are illuminated by UV radiation of the same wavelength, whichone gives off photoelcctrons with the greater maximum kinetic energy? Explain, (b) Calculate the maximum kinetic energy of photoelectrons from each surface if λ = 275 nm.
Solution:
Chapter 30 Quantum Physics Q.32P
White light, with frequencies ranging from 4.00 × 1014 Hz to 7.90 × 1014 Hz, is incident on a potassium surface. Given tha t the work function of potassium is 2.24 eV, find (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.
Solution:
Chapter 30 Quantum Physics Q.33P
Electromagnetic waves, with frequencies ranging from 4.00 × 1014 Hz to 9.00 × 1016 Hz, are incident on an aluminum surface. Given that the work function of aluminum is 4.28 eV, find (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.
Solution:
Chapter 30 Quantum Physics Q.34P
IP Platinum has a work function of 6.35 eV, and iron has a work function of 4.50 eV. Light of frequency 1.88 × 1015 Hz ejects electrons from both of these surfaces, (a) From which surface will the ejected electrons have a greater maximum kinetic energy? Explain, (b) Calculate the maximum kinetic energy of ejected electrons for each surface.
Solution:
Chapter 30 Quantum Physics Q.35P
When light with a frequency f1 = 547.5 THz illuminates a metal surface, the most energetic photoelectrons have 1.260 × 10−19 J of kinetic energy. When light with a frequency f2 = 738.8THz is used Instead, the most energetic photoelectrons have 2.480 × 10−19 J of kinetic energy. Using these experimental results, determine the approximate value of Planck’s constant.
Solution:
Chapter 30 Quantum Physics Q.36P
BIO Owl Vision Owls have large, sensitive eyes for good night vision. Typically, the pupil of an owl’s eye can have a diameter of 8.5 mm (as compared with a maximum diameter of about 7.0 mm for humans). In addition, an owl’s eye is about 100
Solution:
Chapter 30 Quantum Physics Q.37P
CE If the momentum of a particle with finite mass is doubled, its kinetic energy increases by a factor of 4. If the momentum of a photon is doubled, by what factor does its energy increase?
Solution:
Chapter 30 Quantum Physics Q.38P
The photons used in microwave ovens have a momentum of 5.1 × 10−33 kg· m/s.(a) What is their wavelength? (b) How does the wavelength of the microwaves compare with the size of the holes in the metal screen on the door of the oven?
Solution:
Chapter 30 Quantum Physics Q.39P
What speed must an electron have if its momentum is to be the same as that of an X-ray photon with a wavelength of· 0.25 nm?
Solution:
Chapter 30 Quantum Physics Q.40P
What is the wavelength of a photon that has the same momentum as an electron moving with a speed of 1200 m/s?
Solution:
Chapter 30 Quantum Physics Q.41P
What is the frequency of a photon that has the same momentum as a neutron moving with a speed of 1500 m/s?
Solution:
Chapter 30 Quantum Physics Q.42P
A hydrogen atom, initially at rest, emits an ultraviolet photon with a wavelength ofλ = 122 nm. What is the recoil speed of the atom after emitting the photon?
Solution:
Chapter 30 Quantum Physics Q.43P
A blue-green photon (λ = 486 nm) is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen atom after absorbing the photon?
Solution:
Chapter 30 Quantum Physics Q.44P
IP (a) Which has the greater momentum, a photon of red light or a photon of blue light? Explain. (b) Calculate the momentum of a photon of red light (f = 4.0 × 1034 Hz) and a photon of blue light (f = 7.9 × 1014 Hz).
Solution:
Chapter 30 Quantum Physics Q.45P
IP Photon Ahas twice the momentum of photon B. (a) Which photon has the greaterwavelength? Explain, (b) If the wavelength of photon A is 333 nm, what is the wavelength of photon B?
Solution:
Chapter 30 Quantum Physics Q.46P
A laser produces a 5.00-mW beam of light, consisting of photons with a wavelength of 632.8 run. (a) How many photons are emitted by the laser each second? (b) The laser beam strikes a black surface and is absorbed. What is the change in the momentum of each photon that is absorbed? (c) What force does the laser beam exert on the bJack surface?
Solution:
Chapter 30 Quantum Physics Q.47P
A Jaser produces a 7.50-mW beam of light, consisting of photons with a wavelength of 632.8 nm. (a) How many photons are emitted by the laser each second? (b) The laser beam strikes a mirror at normal incidence and is reflected. What is the change in momentum of each reflected photon? Give the magnitude only, (c) What force does the laser beam exert on the mirror?
Solution:
Chapter 30 Quantum Physics Q.48P
CE In a Compton scattering experiment, the scattered elec tron is observed to move in the same direction as the incident X-ray photon. What is the scattering angle of the photon? Explain.
Solution:
Chapter 30 Quantum Physics Q.49P
An X-ray photon has 38.0 keV of energy before it scatters from a free electron, and 33.5 keV after it scatters. What is the kinetic energy of the recoiling electron?
Solution:
Chapter 30 Quantum Physics Q.50P
In the Compton effect, an X-ray photon scatters from a free electron. Find the change in the photon’s wavelength if it scatters at an angle of (a) θ = 30.0°, (b) θ = 90.0°, and (c) θ = 180.0” relative to the incident direction.
Solution:
Chapter 30 Quantum Physics Q.51P
An X-ray scattering from a free electron is observed to change its wavelength by 3.13 pm. At what angle to the incident direction does the scattered X-ray move?
Solution:
Chapter 30 Quantum Physics Q.52P
The maximum Compton shift in wavelength occurs when a photon is scattered through 180°. What scattering angle will produce a wavelength shift of one-fourth the maximum?
Solution:
Chapter 30 Quantum Physics Q.53P
Consider two different photons that scatter through an angle of 180° from a free electron. One is a visible-light photon with λ = 520 nm, the other is an X-ray photon with λ = 0.030 nm. (a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain. (b) Which photon experiences the greater percentage change in wavelength? Explain. (c) Calculate the percentage change in wavelength of each photon.
Solution:
Chapter 30 Quantum Physics Q.54P
An X-ray photon with a wavelength of 0.240 nm scatters from a free electron at rest. The scattered photon moves at an angle of 105° relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.
Solution:
Chapter 30 Quantum Physics Q.55P
An X-ray photon scatters from a free electron at rest at an angle of 175° relative to the incident direction. (a) If the scattered photon has a wavelength of 0.320 nm, what is the wavelength of the incident photon? (b) Determine the energy of the incident and scattered photons. (c) Find the kinetic energy of the recoil electron.
Solution:
Chapter 30 Quantum Physics Q.56P
An X-ray photon scatters through 180° from (i) an electron or (ii) a helium atom. (a) In which case is the change in wavelength of the X-ray greater? Explain. (b) Calculate the change in wavelength for each of these two cases.
Solution:
Chapter 30 Quantum Physics Q.57P
A photon has an energy E and wavelength λ before scattering from a free electron. After scattering through a 135° angle, the photon’s wavelength has increased by 10.0%. Find the initial wavelength and energy of the photon.
Solution:
Chapter 30 Quantum Physics Q.58P
Find the direction of propagation of the scattered electron in Problem 51, given that the incident X-ray has a wavelength of 0.525 nm and propagates in the positive x direction.
Problem
An X-ray scattering from a free electron is observed to change its wavelength by 3.13 pm. At what angle to the incident direction does the scattered X-ray move?
Solution:
Chapter 30 Quantum Physics Q.59P
Predict/Explain (a) As you accelerate your car away from a stoplight, does the de Broglie wavelength of the car increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The de Broglie wavelength will increase because the momentum of the car has increased.
II. The momentum of the car increases. It follows that the de Broglie wavelength will decrease, because it is inversely proportional to the wavelength.
III. The de Broglie wavelength of the car depends only on its mass, which doesn’t change by pulling away from the stoplight. Therefore, the de Broglie wavelength stays the same.
Solution:
Chapter 30 Quantum Physics Q.60P
By what factor does the de Broglie wavelength of a particle change if (a) its momentum is doubled or (b) its kinetic energy is doubled? Assume the particle is nonrelativistic.
Solution:
Chapter 30 Quantum Physics Q.61P
A particle with a mass of 6.69 × 10–27 kg has a de Broglie wavelength of 7.22 pm. What is the particle’s speed?
Solution:
Chapter 30 Quantum Physics Q.62P
What speed must a neutron have if its de Broglie wavelength is to be equal to the interionic spacing of table salt (0.282 nm)?
Solution:
Chapter 30 Quantum Physics Q.63P
A 79-kg jogger runs with a speed of 4.2 m/s. If the jogger is considered to be a particle, what is her de Broglie wavelength?
Solution:
Chapter 30 Quantum Physics Q.64P
Find the kinetic energy of an electron whose de Broglie wavelength is 1.5 Å
Solution:
Chapter 30 Quantum Physics Q.65P
A beam of neutrons with a de Brogue M’a velength of 0.250 nn diffracts from a crystal of table salt, which has an interionic spacing of 0.282 nm. (a) What is the speed of the neutrons? (b) What is the angle of the second interference maximum?
Solution:
Chapter 30 Quantum Physics Q.66P
IP An electron and a proton have the same speed, (a) Which has the longer de Broglie wavelength? Explain. (b) Calculate the ratio (λe/λp).
Solution:
Chapter 30 Quantum Physics Q.67P
IP An electron and a proton have the same de Broglie wavelength, (a) Which has the greater kinetic energy? Explain. (b) Calculatethe ratio of the electron’s kinetic energy to the kinetic energy of the proton.
Solution:
Chapter 30 Quantum Physics Q.68P
Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted, (a) At what speed will the de Broglie wavelength of a 65-kg student be equal to the 0.76-m width of a doorway? (b) At this speed, how long will it take the student to travel a distance of 1.0 mm? (For comparison, the age of the universe is approximately 4 × 1017s.)
Solution:
Chapter 30 Quantum Physics Q.69P
A particle has a mass m and an electric charge q. The particle is accelerated from rest through a potential difference V. What is the particle’s de Broglie wavelength, expressed in terms of m, q, and V?
Solution:
Chapter 30 Quantum Physics Q.70P
A baseball (0.15 kg) and an electron both have a speed of 41 m/s. Find the uncertainty in position of each of these objects, given that the uncertainty in their speed is 5.0%.
Solution:
Chapter 30 Quantum Physics Q.71P
The uncertainty in position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus, If this diameter is 7.5 × 10−15, what is the uncertainty in the proton’s momentum?
Solution:
Chapter 30 Quantum Physics Q.72P
“ The position of a 0.26-kg air-track cart is determined to within an uncertainty of 2.2 nun. What speed must the cart acquire as a result of the position measurement?
Solution:
Chapter 30 Quantum Physics Q.73P
The measurement of an electron’s energy requires a time interval of 1.0 × 10–8 s. What is the smallest possible uncertainty in the electron’s energy?
Solution:
Chapter 30 Quantum Physics Q.74P
A particle’s energy is measured with an uncertainty of 0.0010 eV. What is the smallest possible uncertainty in our knowledge of when the particle had this energy?
Solution:
Chapter 30 Quantum Physics Q.75P
An excited state of a particular atom has a mean lifetime of 0.60 × 10–9 s, which we may take as the uncertainty Δt. What is the minimum uncertainty in any measurement of the energy of this state?
Solution:
Chapter 30 Quantum Physics Q.76P
The ∑+ is an unstable particle, with a mean lifetime of 2.5 × 10–10 s. Its lifetime defines the uncertainty ∆t for this particle. What is the minimum uncertainty in this particle’s energy?
Solution:
Chapter 30 Quantum Physics Q.77P
The uncertainty in an electron’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty (∆p = p)?
Solution:
Chapter 30 Quantum Physics Q.78P
The uncertainty in a proton’s position is 0.15 nm. (a) What is the minimum uncertainty ∆p in its momentum? (b) What is the kinetic energy of a proton whose momentum is equal to this uncertainty (∆p = p)?
Solution:
Chapter 30 Quantum Physics Q.79P
An electron has a momentum p ≈ 1.7 × 10–25kg · m/s. What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum (∆p/p) below 1.0%?
Solution:
The Heisenberg’s uncertainty principle in terms of momentum and position is,
Chapter 30 Quantum Physics Q.80GP
CE Suppose youperform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the intensity of the light is increased while the frequency is held constant, describe whether the following quantities increase,, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.
Solution:
Chapter 30 Quantum Physics Q.81GP
CE Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increase, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.
Solution:
Chapter 30 Quantum Physics Q.82GP
CE An electron that is accelerated from rest through a potential difference V0 has a de Broglie wavelength λ0. What potential difference will double the electron’s wavelength? (Express your answer in terms of V0.)
Solution:
Chapter 30 Quantum Physics Q.83GP
CE A beam of particles diffracts from a crystal, producing an interference maximum at the angle θ. (a) If the mass of the particles is increased, with every thing else remainingthe same, does the angle of the interference maximum increase, decrease, or stay the same? Explain (b). If the energy of the particles is increased, with every tiling else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain.
Solution:
Chapter 30 Quantum Physics Q.84GP
You want to construct a photocell that works with visible light. Three materials are readily available: aluminum (W0 = 4.28 eV), lead (W0 = 4.25 eV), and cesium (W0 = 2.14 eV). Which materials) would be suitable?
Solution:
Chapter 30 Quantum Physics Q.85GP
BIO Human Vision Studies have shown that some people can detect 545-nm light with as few as 100 photons entering the eye per second. Wha t is the power delivered by such a beam of light?
Solution:
Chapter 30 Quantum Physics Q.86GP
A pendulum consisting of a 0.15-kg mass attached to a 0.78-m string undergoes simple harmonic motion, (a) What is the frequency of oscillation for this pendulum? (b) Assuming the energy of this system satisfies En = nhf, find the maximum speed of the 0.15-kg mass when the quantum number is 1.0 × 1033.
Solution:
Chapter 30 Quantum Physics Q.87GP
To listen to a radio station, a certain home receiver must pick up a signal of at least 1.0 × 10−10 W. (a) If the radio waves have a frequency of 96 MHz, how many photons must the receiver absorb per second to get the station? (b) How much force is exerted on the receiving antenna for the case considered in part (a)?
Solution:
Chapter 30 Quantum Physics Q.88GP
The latent heat for converting ice at0°C to water at 0°C is 80.0 kcal/kg (Chapter 17). (a.) How many photons of frequency 6.0 × 101.1 Hz must be absorbed by a 1.0-kg block of ice at 0 °C to melt it to water at 0 °C? (b) How many molecules of H2O can one photon convert from ice to water?
Solution:
Chapter 30 Quantum Physics Q.89GP
How many 550-nm photons would have to be absorbed to raise the temperature of 1.0 g of water by 1.0 C°?
Solution:
Chapter 30 Quantum Physics Q.90GP
A microwave oven can heat 205 ml of water from 20.0 °C to 90.0 °C in 2.00 min. If the wavelength of the microwaves is λ= 12.2 cm, how many photons were absorbed by the water? (Assume no loss of heat by the water.)
Solution:
Chapter 30 Quantum Physics Q.91GP
Light with a frequency of 2.11 × 1015 Hz ejects electrons from the surface of lead, which has a work function of 4.25 eV. What is the minimum de Broglie wavelength of the ejected electrons?
Solution:
Chapter 30 Quantum Physics Q.92GP
An electron moving with a speed of 2.7 × 106 m/s has the same momentum as a photon. Find (a) the de Broglie wavelength of the electron and (b) the wavelength of the photon.
Solution:
Chapter 30 Quantum Physics Q.93GP
BIO The Cold Light of Fireflies Fireflies are often said to give off “cold light.” Given that the peak ina firefly’s radiation occurs at about 5.4 × 1014 Hz, determine the temperature of a blackbody that would have the same peak frequency. From your result, would you say that firefly radiation is well approximated by blackbody radiation? Explain.
Solution:
Chapter 30 Quantum Physics Q.94GP
IP When light with a wavelength of 545 runshines on a metal surface, electrons are ejected with speeds of 3.10 × 105 m/s or less. (a) Give a strategythat allows you to use the preceding information to calculate the work function and cutoff frequency for this surface. (b) Carry out your strategy and determine the work function and cutoff frequency.
Solution:
Chapter 30 Quantum Physics Q.95GP
IP A hydrogen atom absorbs a 486.2-nrn photon. A short time later, the same atom emits a photon with a wavelength of 97.23 nm. (a) Has the net energy of the atom increased or decreased? Explain. (b) Calculate the change in energy of the hydrogen atom.
Solution:
Chapter 30 Quantum Physics Q.96GP
When a beam of atoms emerges from an oven at the absolute temperature T, the most probable de Broglie wavelength for a given atom is
In this expression, m is the mass of an atom, and k is Boltz-mann’s constant (Chapter). What is the most probable speed of a hydrogen atom emerging from an oven at 450 K?
Solution:
Chapter 30 Quantum Physics Q.97GP
Solution:
Chapter 30 Quantum Physics Q.98GP
A jar is filled with monatomic helium gas at a temperature of 25 °C. The pressure inside the jar is one atmosphere; that is, 101 kPa. (a) Find the average de Broglie wavelength of the he-Hum atoms. (b) Calculate the average separation between helium atoms in the jar. (Note: The fact that the spacing between atoms is much greater than the de Broglie wavelength means quantumeffects are negligible, and the atoms can be treated as particles.)
Solution:
Chapter 30 Quantum Physics Q.99GP
The Compton Wavelength The Compton wavelength, λC, of a particle of mass m is defined as follows: λC = h/mc. (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part
(a), (c) Show, in general, that a photon with a “wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.
Solution:
Chapter 30 Quantum Physics Q.100GP
IP Light of frequency 8.22 × 1014 Hz ejects electrons from surface A with a maximum kinetic energy that is 2.00 × 10−19 J greater than the maximum kinetic energy of electrons ejected from surface B. (a) If the frequency of the light is increased, does the difference in maximum kinetic energy observed from, the two surfaces increase, decrease, or stay the same? Explain. (b) Calculate the difference in work function for these two surfaces.
Solution:
Chapter 30 Quantum Physics Q.101PP
What is the work function, W0, for lithium, as determined from Millikan’s results?
A. 0.0112 eV
B. 0.951 eV
C. 1.63 eV
D. 2.29 eV
Solution:
Chapter 30 Quantum Physics Q.102PP
What value does Millikan obtain for Planck’s constant, based on the lithium measurements? (His value is close to, but not the same as, the currently accepted value.)
A. 1.12 × 10−34 J· s
B. 3.84 × 10−34 J· s
C. 6.14 × 10−34 J· s
D. 6.57 × 10−34 J· s
Solution:
Chapter 30 Quantum Physics Q.103PP
What maximum kinetic energy do you predict Millikan found when he used light with a wavelength of 365.0 nm?
A. 0.805 eV
B. 1.08 eV
C. 2.29 eV
D. 2.82 eV
Solution:
Chapter 30 Quantum Physics Q.104IP
IP Referring to Example 30–4 An X-ray photon with λ = 0.6500 nm scatters from an electron, giving the electron a kinetic energy of 7.750 eV. (a) Is the scattering angle of the photon greater than, less than, or equal to 152°? (b) Find the scattering angle.
Solution:
Chapter 30 Quantum Physics Q.105IP
IP Referring to Example 30–4 An X-ray photon with λ = 0.6500 nm scatters from an electron. The wavelength of the scattered photon is 0.6510 nm. (a) Is the scattering angle in this case greater than, less than, or equal to 152°? (b) Find the scattering angle.
Solution:
